{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import igraph as ig\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "g = ig.Graph(\n",
    "    6,\n",
    "    [(3, 2), (3, 4), (2, 1), (4,1), (4, 5), (1, 0), (5, 0)],\n",
    "    directed=True\n",
    ")\n",
    "g.es[\"capacity\"] = [7, 8, 1, 2, 3, 4, 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>vertex ID</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: []\n",
       "Index: [0, 1, 2, 3, 4, 5]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.get_vertex_dataframe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>source</th>\n",
       "      <th>target</th>\n",
       "      <th>capacity</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>edge ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         source  target  capacity\n",
       "edge ID                          \n",
       "0             3       2         7\n",
       "1             3       4         8\n",
       "2             2       1         1\n",
       "3             4       1         2\n",
       "4             4       5         3\n",
       "5             1       0         4\n",
       "6             5       0         5"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.get_edge_dataframe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ig.plot(\n",
    "    g,\n",
    "    target=ax,\n",
    "    layout=\"circle\",\n",
    "    vertex_label=range(g.vcount()),\n",
    "    vertex_color=\"lightblue\"\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max flow: 6.0\n",
      "Edge assignments: [1.0, 5.0, 1.0, 2.0, 3.0, 3.0, 3.0]\n"
     ]
    }
   ],
   "source": [
    "flow = g.maxflow(3, 0, capacity=g.es[\"capacity\"])\n",
    "\n",
    "print(\"Max flow:\", flow.value)\n",
    "print(\"Edge assignments:\", flow.flow)\n",
    "\n",
    "# Output:\n",
    "# Max flow: 6.0\n",
    "# Edge assignments [1.0, 5.0, 1.0, 2.0, 3.0, 3.0, 3.0]"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.6 ('py310')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "49ec5068d4d6d3736c39d3918a16f1ca551a23384109b69898c01c2015d1370c"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
